Calculate the stress in a tight wire of a material whose Young's modulus is 19 . 6 × 10 11 dyne/cm 2 so that the speed of the longitudinal waves is 10 times the speed of transverse waves.

The speed of transverse waves in the string is given by the relation: c 1 = T m = T A d Here, A is the cross-sectional area and d is the density. The speed of longitudinal waves in string is c 2 = Y / d . Also, we have, c 2 = 10 c 1 ⇒ Y d = 10 T A d ⇒ Stress = T A = Y 100 = 19 . 6 × 10 9 dyne / cm 2 Hence, the stress in the wire is 19 . 6 × 10 9 dyne / cm 2

Calculate the stress in a tight wire of a material whose Young's modulus is 19 . 6 × 10 11 dyne/cm 2 so that the speed of the longitudinal waves is 10 times the speed of transverse waves.

The speed of transverse waves in the string is given by the relation: c 1 = T m = T A d Here, A is the cross-sectional area and d is the density. The speed of longitudinal waves in string is c 2 = Y / d . Also, we have, c 2 = 10 c 1 ⇒ Y d = 10 T A d ⇒ Stress = T A = Y 100 = 19 . 6 × 10 9 dyne / cm 2 Hence, the stress in the wire is 19 . 6 × 10 9 dyne / cm 2

Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz , respectively. A car is initially at a point P , 1800 m away from the midpoint Q of the line M N and moves towards Q constantly at 60 km h - 1 along the perpendicular bisector of M N . It crosses Q and eventually reaches a point R , 1800 m away from Q . Let ν t represent the beat frequency measured by a person sitting in the car at time t . Let ν p , ν Q and ν R be the beat frequencies measured at locations P , Q and R , respectively. The speed of sound in air is 330 m s - 1 . Which of the following statement(s) is (are) true regarding the sound heard by the person?

The plot below represents schematically the variations of beat frequency with time

Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. The wind blows along the road with velocity w . One of these vehicles blows a whistle of frequency f 1 . An observer in the other vehicle hears the frequency of the whistle to be f 2 . The speed of sound in still air is v . The correct statement (s) is (are):

If the wind blows from the source to the observer, f 2 > f 1 .

If the wind blows from the observer to the source, f 2 < f 1 .

If the wind blows from the source to the observer, f 2 < f 1 .

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Physics

IMPORTANT

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Calculate the stress in a tight wire of a material whose Young's modulus is $19.6 \times 10^{11} {dyne/cm}^{2}$ so that the speed of the longitudinal waves is $10$ times the speed of transverse waves.

Important Questions on Sound Waves and Doppler Effect

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 8 - Sound Waves and Doppler Effect>ILLUSTRATIONS>Q 8.5

Taking the composition of air to be

75 %

of nitrogen and

25 %

of oxygen by weight, calculate the velocity of sound through air.

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 8 - Sound Waves and Doppler Effect>ILLUSTRATIONS>Q 8.6

If the speed of sound through hydrogen is

1280 m / s

, what will be the speed of sound through a mixture of

4

parts by volume of hydrogen and

1

part of oxygen? Given density of oxygen is

16

times that of hydrogen.

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 8 - Sound Waves and Doppler Effect>ILLUSTRATIONS>Q 8.7

A certain gas mixture is composed of two diatomic gases (molecular weights

M_{1}

and

M_{2}

). The ratio of the masses of the two gases in a given volume is

m_{2} / m_{1} = r .

Find the speed of sound in the gas mixture if the gases are ideal.

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 8 - Sound Waves and Doppler Effect>ILLUSTRATIONS>Q 8.8

The figure shows an instantaneous displacement-position graph of a sound wave travelling along the positive $x$ -axis. Identify the points of

Question Image

maximum pressure;

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 8 - Sound Waves and Doppler Effect>ILLUSTRATIONS>Q 8.8

The figure shows an instantaneous displacement-position graph of a sound wave travelling along the positive $x$ -axis. Identify the points of

Question Image

minimum pressure and

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 8 - Sound Waves and Doppler Effect>ILLUSTRATIONS>Q 8.8

The figure shows an instantaneous displacement-position graph of a sound wave travelling along the positive $x$ -axis. Identify the points of

Question Image

atmospheric pressure (or normal pressure).

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 8 - Sound Waves and Doppler Effect>ILLUSTRATIONS>Q 8.9

Corresponding to displacement equation, $y = A \sin (k x + ω t)$ of a longitudinal wave make its pressure and density wave also. Bulk modulus of the medium is $B$ and density is $ρ$ .

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 8 - Sound Waves and Doppler Effect>ILLUSTRATIONS>Q 8.10

If the maximum tolerable pressure variation in sound is undefined at

1000 Hz

. Find the amplitude of density and displacement. Given: Bulk modulus of medium

B = 1.4 \times 10^{5} Pa

, density of the medium

ρ = 1.20 kg / m^{3}

and speed of sound

= 341 m / s

Calculate the stress in a tight wire of a material whose Young's modulus is 19.6×1011 dyne/cm 2 so that the speed of the longitudinal waves is 10 times the speed of transverse waves.

Important Questions on Sound Waves and Doppler Effect

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Calculate the stress in a tight wire of a material whose Young's modulus is $19.6 \times 10^{11} {dyne/cm}^{2}$ so that the speed of the longitudinal waves is $10$ times the speed of transverse waves.