Question

sound wave of wavelength 5m and 6m produce 30 beats in 3sec The velocity of sound is??

300m/s 310m/s
330n/s 330m/s​

Answer 1

Let the speed of Sound be v.

Beat Frequency = 30/3 = 10 Hz (1)

But Beat Frequency = | f1 - f2 | (2)

Since fλ = v

f1 = v/5

f2 = v/6

from (1) and (2)

|v/5 - v/6| = 10

v = 300 m/s

Answer 2

The velocity of sound is 300 m/s.

Explanation:

It is given that,

Wavelength of sound wave 1, $\lambda_1=5\ m$

Wavelength of sound wave 2, $\lambda_2=6\ m$

Number of beats produced is 30

Time, t = 3 s

The beat frequency is given by :

$f_2-f_1=\dfrac{30}{3}=10$

Since, $f=\dfrac{v}{\lambda}$

$\dfrac{v}{\lambda_2}-\dfrac{v}{\lambda_1}=10$

$v(\dfrac{1}{\lambda_2}-\dfrac{1}{\lambda_1})=10$

$v(\dfrac{1}{6}-\dfrac{1}{5})=10$

v = 300 m/s

So, the velocity of sound is 300 m/s. Hence, this is the required solution.

Learn more,

Speed of sound wave

https://brainly.in/question/5426438