Question

14. A sound wave whose frequency is 5000Hz travels in air
and the hits the water surface. The ratio of its wavelength
in water and air is
a) 4.30 6) 0.23 c) 5.30 d) 1.23​

Answer 1

Answer :

➡4.30

Explaination :

Given ,

Frequency of sound wave = 5000 Hz

As we know that ,

Speed of sound in water = 1550 m/s

Speed of sound in air = 343 m/s

$\star \: \: \purple{ \sf \fbox{Wavelength = \frac{speed }{frequency} }}$

Wavelength in water

$\implies \sf Wavelength = \frac{1550}{5000} \\ \\ \sf \implies Wavelength= 0.31 \: \: m$

Wavelength in air

$\implies \sf Wavelength = \frac{343}{5000} \\ \\ \sf \implies Wavelength= 0.0686 \: \: m$

Thus , the ratio of wavelength in water and air is

$\sf = \frac{0.31}{0.0686} \\ \\ \sf = 4.30 \: \: \{approx \}$

Hence , the correct option is (a) 4.30

Answer 2

The ratio of wavelength  in water and air is 4.31.

Explanation:

Given that,

Frequency of sound wave, f = 5000 Hz

The sound wave travels in air  and the hits the water surface.

We know that the speed of sound in air is, $v_1=343\ m/s$

The speed of sound in water is, $v_2=1550\ m/s$

The formula of the speed of sound is given by :

$v=f\lambda$

f is same or both conditions

The ratio of its wavelength  in water and air is :

$\dfrac{v_2}{v_1}=\dfrac{\lambda_2}{\lambda_1}\\\\\dfrac{\lambda_2}{\lambda_1}=\dfrac{1550}{343}\\\\\dfrac{\lambda_2}{\lambda_1}=4.31$

So, the ratio of wavelength  in water and air is 4.31. Hence, the correct option is (a).

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