Question

A sound source of frequency 29,000 Hz in air. If the sound meets a water surface, it gets partially reflected back and partially refracted (transmitted) in water. Difference of wavelength transmitted to wavelength reflected will be: (speed of sound in air= 340 m/s. Bulk modulus of water= 2.25*10^9 N/m^2 , r (water)= 1000 kg/m^3)

Answer 1

Answer:

(a) Frequency of the ultrasonic sound, f=1000kHz=10

6

Hz

Speed of sound in air, V

a

=340m/s

The wavelength (λ

r

) of the reflected sound is given by the relation:

λ

r

=V/f

=340/10

6

=3.4×10

−4

m.

• (b) Frequency of the ultrasonic sound, f=1000kHz=10

6

Hz

Speed of sound in water, V

w

=1486 m/s

1. The wavelength of the transmitted sound is given as:

λ

r

=1486/10

6

=1.49×10

−3

m.

Answer 2

The difference between wavelength transmitted to wavelength reflected is 0.04m.

Given:

A sound source of frequency 29,000 Hz in air. If the sound meets a water surface, it gets partially reflected back and partially refracted (transmitted) in water.

To Find:

Difference of wavelength transmitted to wavelength reflected.

Solution:

To find the difference between wavelength transmitted to wavelength reflected we will follow the following steps:

As we know,

Velocity, wavelength and frequency relation is:

$λ \: = \frac{velocity}{frequency}$

Now,

Reflected sound wavelength is wavelength in air. so,

$λair = \frac{340}{29000} = 0.0117m$

Also,

Velocity in water =

$velocity \: = \sqrt{ \frac{β}{ρ} } = \sqrt{ \frac{2.25 \times {10}^{9} }{1000} } = 1.5 \times {10}^{3} = 1500m {s}^{ - 1}$

Now,

$λwater = \frac{1500}{29000} = 0.0517m$

The difference in wavelength in water and air = λwater - λair = 0.0517 - 0.0117 = 0.04m.

Henceforth, the difference between the wavelength transmitted and the wavelength reflected is 0.04m.

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