For the standing observer: Frequency is given as $\mathrm{v}_{\mathrm{H}}=200 \mathrm{~Hz}$ Velocity of sound is given as $v=340 \mathrm{~m} / \mathrm{s}$ Speed of the wind is given as $v_{w}=20...

### A man standing at a certain distance from an observer blows a horn of frequency in still air.

(a) Find the horn’s frequency for the observer when the man (i) runs towards him at (ii) runs away from him at .

(b) Find the speed of sound in both the cases.

[Speed of sound in still air is

Frequency of the horn is given as $\mathrm{v}_{\mathrm{H}}=200 \mathrm{~Hz}$ Velocity of the man is given as $\mathrm{v}_{\mathrm{T}}=20 \mathrm{~m} / \mathrm{s}$ Velocity of sound is given as...

### A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is . During one fast swoop directly toward a flat wall surface, the bat is moving at times the speed of sound in the air. What frequency does the bat hear reflected off the wall?

The sound emission frequency of the bat is given as $=40 \mathrm{kHz}$ The velocity of the bat is given as $v_{b}=0.03 \mathrm{v}$ Here, the velocity of the sound in air is $v$ The apparent...

### Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of the S wave is about , and that of the wave is . A seismograph records and waves from an earthquake. The first P wave arrives 4 min before the first wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?

Let $S$ and $P$ have speeds of $v_{1}$ and $v_{2}$, respectively. The $S$ and $P$ waves take $t_{1}$ and $t_{2}$ seconds to reach the position of the seismograph, respectively. $I=v_{1} t_{1}=v_{2}...

### A SONAR system fixed in a submarine operates at a frequency kHz. An enemy submarine moves towards the SONAR with a speed of . What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be .

Frequency of the SONAR system is given as $\mathrm{f}=40 \mathrm{kHz}=40 \times 10^{3} \mathrm{~Hz}$ Speed of sound in water is given as $v=1450 \mathrm{~m} / \mathrm{s}$ Speed of the enemy...

### One end of a long string of linear mass density is connected to an electrically driven tuning fork of frequency . The other end passes over a pulley and is tied to a pan containing a mass of . The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At , the left end (fork end) of the string has zero transverse displacement and is moving along positive -direction. The amplitude of the wave is . Write down the transverse displacement y as a function of and that describes the wave on the string.

Linear mass density of the string is given as $\mu=8.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$ Frequency of the tuning fork is given as $=256 \mathrm{~Hz}$ Mass on the pan is given as $90...

### A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium. (a) Does the pulse have a definite (i) frequency, (ii) wavelength, (iii) speed of propagation? (b) If the pulse rate is 1 after every , (that is the whistle is blown for a split of second after every ), is the frequency of the note produced by the whistle equal to or ?

(a) The speed of propagation is known, and it is the same as the speed of sound in air. The wavelength and frequency of the signal will be uncertain. (b) The note emitted by a whistle does not have...

### A travelling harmonic wave on a string is described by

(a) What are the displacement and velocity of oscillation of a point at , and ? Is this velocity equal to the velocity of wave propagation?

(b) Locate the points of the string which have the same transverse displacements and velocity as the point at and

(a) The travelling harmonic wave is given by, $y(x, t)=7.5 \sin (0.0050 x+12 t+\pi / 4)$ At $x=1 \mathrm{~cm}$ and $\mathrm{t}=1 \mathrm{~s}$ $y(1,1)=7.5 \sin (0.0050(1)+12(1)+\pi / 4)$ $=7.5 \sin...

### A train, standing in a station-yard, blows a whistle of frequency in still air. The wind starts blowing in the direction from the yard to the station with a speed of . What are the frequency, wavelength, and speed of sound for an observer standing on the station’s platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of ? The speed of sound in still air can be taken as

Frequency of the whistle is given as $400 \mathrm{~Hz}$ Speed of wind is given as $\mathrm{v}_{\mathrm{w}}=10 \mathrm{~m} / \mathrm{s}$ Speed of sound in still air is given as $v= 340 \mathrm{~m} /...

### A train, standing at the outer signal of a railway station blows a whistle of frequency in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of , (b) recedes from the platform with a speed of ? (ii) What is the speed of sound in each case? The speed of sound in still air can be taken as .

Frequency of the whistle is given as $=400 \mathrm{~Hz}$ Speed of sound in still air is given as $=340 \mathrm{~m} / \mathrm{s}$ (i) (a)Train approaches the platform at a speed given as...

### Explain how:

In a dispersive medium, the shape of a pulse propagating through it gets distorted.

A pulse is made up of electromagnetic waves with different wavelengths. In a dispersive medium, these waves flow at various speeds. Its shape is distorted as a result of this.

### Explain how:

(i) A guitar note and violin note are being played at the same frequency, however, we can still make out which instrument is producing which note

(ii) Both transverse and longitudinal wave can propagate through solids, but only longitudinal waves can move through gases.

(i) Overtones are produced differently by the guitar and the violin. Even though the notes from a guitar and a violin vibrate at the same frequencies, it is possible to distinguish between them....

### Explain how:

(i) A sound wave’s pressure antinode is a displacement node and vice versa.

(ii) The Ganges river dolphin despite being blind, can manoeuvre and swim around obstacles and hunt down preys.

(i) An antinode is a place where the pressure is lowest and the vibration amplitude is highest. A node, on the other hand, is a place where pressure is highest and vibration amplitude is lowest....

### Guitar strings and striking the note ‘Ga’ are a little out of tune and give beats at . When the string is slightly loosened and the beat frequency becomes . Given that the original frequency of is , find the frequency of .

Frequency of $\mathrm{X}$ is given as $\mathrm{f}_{\mathrm{x}}=324 \mathrm{~Hz}$ Frequency of $Y$ is given as $f_{Y}$ Frequency of the beat is given as $\mathrm{n}=6 \mathrm{~Hz}$ Also,...

### One end of A long tube is closed. Find the harmonic mode of the tube that will be resonantly excited by a source of frequency . If both the ends are open, can the same source still produce resonance in the tube? (Sound travels in air at ).

Length of the pipe is given as $I=20 \mathrm{~cm}=0.2 \mathrm{~m}$ Frequency of the source is given as $\mathrm{n}^{\text {th }}$ Normal mode of frequency is given as $\mathrm{v}_{\mathrm{N}}=430...

### A steel bar of length is nailed at its midpoint. The fundamental frequency of the longitudinal vibrations of the rod is . At what speed will the sound be able to travel through steel?

Length is given as $I=200 \mathrm{~cm}=2 \mathrm{~m}$ Fundamental frequency of vibration is given as, $\mathrm{v}_{\mathrm{F}}=2.53 \mathrm{kHz}=2.53 \times 10^{3} \mathrm{~Hz}$ The bar is then...

### A long pipe with a movable piston at one end and an opening at the other will be in resonance with a tuning fork vibrating at , if the length of the pipe is or . Calculate the speed of sound in air. Neglect the edge effects.

Frequency of the turning fork is given as $\mathrm{v}_{\mathrm{F}}=340 \mathrm{~Hz}$ Length of the pipe is given as $l_{1}=0.255 \mathrm{~m}$ Due to the presence of a piston at one end, the supplied...

### A string clamped at both its ends is stretched out, it is then made to vibrate in its fundamental mode at a frequency of . The linear mass density of the string is m and its mass is kg. Calculate:

(i) the velocity of a transverse wave on the string,

(ii) the tension in the string.

Mass of the string is given as $m=2 \times 10^{-2} \mathrm{~kg}$ Linear density of the string is given s $=4 \times 10^{-2} \mathrm{~kg}$ Frequency is given as $\mathrm{v}_{\mathrm{F}}=45...

### Present below are functions of and to describe the displacement (longitudinal or transverse) of an elastic wave. Identify the ones describing ( a ) a stationary wave, ( b ) a travelling wave and ( c) neither of the two:

(i)

(ii)

(i) Because the harmonic terms $\omega t$ and $k x$ exist individually, this equation depicts a stationary wave. (ii) There are no harmonic terms in this equation. As a result, it is neither a...

### Present below are functions of and to describe the displacement (longitudinal or transverse) of an elastic wave. Identify the ones describing ( a ) a stationary wave, ( b ) a travelling wave and ( c) neither of the two:

(ii)

(i) The harmonic terms $\omega t$ and $kx$ in the combination of $k x-w t$ explain a traveling wave in this equation. (ii) The harmonic terms $\omega t$ and $kx$ exist individually in the equation....

### Considering the wave,

Answer the following questions;

(a) Are all the points in the wire oscillating at the same values of (i) frequency, (ii) phase, (iii) amplitude? Justify your answers.

(b) Calculate the amplitude of a point away from one end?

(a) Because both ends of the wire are clamped, the ends act as nodes, and the entire wire vibrates as a single segment. Thus, (i) Except at the wire's ends, where the frequency is 0, all of the...

### The transverse displacement of a wire (clamped at both its ends) is described as : The mass of the wire is and its length is .

Provide answers to the following question:

Calculate the wire’s tension.

[X and are in meters and in secs]

As we know, The standard equation of a stationary wave is known as, $y(x, t)=2 a \sin k x \cos w t$ Given equation is, $y(x, t)=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$ It is...

### The transverse displacement of a wire (clamped at both its ends) is described as : The mass of the wire is and its length is .

Provide answers to the following questions:

(i) Is the function describing a stationary wave or a travelling wave?

(ii) Interpret the wave as a superposition of two waves travelling in opposite directions. Find the speed, wavelength and frequency of each wave.

As we know, The standard equation of a stationary wave is known as, $y(x, t)=2 a \sin k x \cos w t$ Given equation is, $y(x, t)=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$ It is...

### A travelling harmonic wave is given as: . What is the phase difference between the oscillatory motion of two points separated by a distance of:

(i) ,

(ii)

[ and are in and is in secs .

Equation for a travelling harmonic wave is given as, $\begin{array}{l} y(x, t)=2.0 \cos 2 \pi(10 t-0.0080 x+0.35) \\ =2.0 \cos (20 \pi t-0.016 \pi x+0.70 \pi) \end{array}$ where, Propagation...

### A travelling harmonic wave is given as: . What is the phase difference between the oscillatory motion of two points separated by a distance of:

(i) ,

(ii)

[ and are in and is in secs .

Equation for a travelling harmonic wave is given as, $\begin{array}{l} y(x, t)=2.0 \cos 2 \pi(10 t-0.0080 x+0.35) \\ =2.0 \cos (20 \pi t-0.016 \pi x+0.70 \pi) \end{array}$ where, Propagation...

### For the wave, plot the displacement ( ) versus (t) graphs for 0,2 and .

(i) Give the shapes of these plots.

(ii) With respect to which aspects (amplitude, frequency or phase) does the oscillatory motion in a travelling wave differ from one point to another?

Given wave is, $y(x, t)=3 \sin (36 t+0.018 x+\pi / 4)$.....(1) Putting $x=0$, the equation becomes: $y(0, t)=3 \sin (36 t+0+\pi / 4)$.....(2) Also, $\omega=2 \pi / \mathrm{t}=36 \mathrm{rad} /...

### A transverse harmonic wave on a wire is expressed as:

Calculate the smallest distance between two adjacent crests in the wave.

[ and are in and in seconds. Assume the left to right direction as the positive direction of

Given function is, $(x, t)=3 \sin (36 t+0.018 x+\pi / 4)$ The smallest distance between two adjacent crests in the wave can be calculated as, $\lambda=2 \pi / \mathrm{k}=2 \mathrm{~m} / 0.018$ $=349...

### A transverse harmonic wave on a wire is expressed as:

i) Find its frequency and amplitude.

ii) Give the initial phase at the origin.

[ and are in and in seconds. Assume the left to right direction as the positive direction of

Given function is, $(x, t)=3 \sin (36 t+0.018 x+\pi / 4)$ i) Amplitude of the wave is given as $a=3 \mathrm{~cm}$ Frequency of the wave can be calculated as $v=\omega / 2 \pi$ $36 / 2 \pi=5.7...

### A transverse harmonic wave on a wire is expressed as:

(i) Is it a stationary wave or a travelling one?

ii) If it is a travelling wave, give the speed and direction of its propagation.

[ and are in and in seconds. Assume the left to right direction as the positive direction of

Given function is, $(x, t)=3 \sin (36 t+0.018 x+\pi / 4)$ i) The equation of a progressive wave travelling from right to left is known as, $y(x, t)=a \sin (\omega t+k x+\Phi)$ On comparing equation...

### An ultrasonic scanner operating at is used to locate tumours in tissues. If the speed of sound is in a certain tissue, calculate the wavelength of sound in this tissue.

Speed of sound in the tissue is given as, $v_{T}=2 \mathrm{~km} / \mathrm{s}=2 \times 10^{3} \mathrm{~m} / \mathrm{s}$ Operating frequency of the scanner is given as $\mathrm{v}=4.2 \mathrm{MHz}=4.2...

### A bat emits ultrasonic sound of frequency in air. If the sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound? Speed of sound in air is and in water

Frequency of the ultrasonic sound is given as $\mathrm{v}=1000 \mathrm{kHz}=10^{6} \mathrm{~Hz}$ Speed of sound in air is given as $v_{A}=340 \mathrm{~m} / \mathrm{s}$ As we know, (a) The wavelength...

### We know that the function represents a wave travelling in one direction, where and must appear in the combination or or i.e. Is the converse true? Can the following functions for y possibly represent a travelling wave:

(i)

(ii)

(iii)

No, the opposite is not true, because a wave function representing a travelling wave must have a finite value for all $x$ and $t$ values. None of the functions above satisfy the criteria, hence none...

### Using the formula explain why the speed of sound in air increases with humidity.

Given values are, $v=\sqrt{\frac{\gamma P}{\rho}}$ $\Rightarrow \mathrm{P}=\frac{\rho R T}{M}$ $\Rightarrow \frac{P}{\rho}=\frac{R T}{M}$ The effective density of the air decreases as humidity...

### Using the formula explain why the speed of sound in air

(a) does not depend upon pressure.

(b) increases with temperature and humidity.

Given values are, $v=\sqrt{\frac{\gamma P}{\rho}}$ $\Rightarrow \mathrm{P}=\frac{\rho R T}{M}$ $\Rightarrow \frac{P}{\rho}=\frac{R T}{M}$ (a) For a gas at a constant temperature, $\frac{P}{\rho}=...

### Steel wire has a length of and a mass of What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at

Length of the steel wire is given as $I=12 \mathrm{~m}$ Mass of the steel wire is given as $\mathrm{m}=2.0 \mathrm{~kg}$ Velocity of the transverse wave is given as $\mathrm{v}=343 \mathrm{~m} /...

### A stone dropped from the top of a tower of height splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is ?

Height of the bridge is given as $s=300 \mathrm{~m}$ Initial velocity of the stone is given as $u=0$ Acceleration is known as $a=g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ Speed of sound in air is given as...

### A string of mass is under a tension of . The length of the stretched string is . If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?

Mass of the string is given as $M=2.50 kg$ Tension in the string is given as $T=200 N$ Length of the string is given as $\mid=20.0 m$ Mass per unit length will be, $\mu=\mathrm{M} / \mathrm{I}=5 /...