Question

Two sound waves having wavelengths of 87 cm and 88.5cm respectively, when superimposed, produce 10 beats per second. Find the velocity of sound (Ans : 513.3 m/s)

Answer 1

wavelength of first sound , $\lambda_1$ = 87cm = 0.87m
wavelength of 2nd sound, $\lambda_2$ = 88.5cm = 0.885m

we know, $v=n\lambda$
so, frequency is inversely proportional to wavelength.
so, frequency of first ever is higher than frequency of 2nd wave.

given, number of beats per second = 10
so, $n_2-n_1=10$

or, $\frac{v}{\lambda_1}-\frac{v}{\lambda_2}=10$

or, v(1/0.87 - 1/885) = 10

after solving it we get, v = 513.3 m/a

Answer 2

Answer:

Two sound waves having wavelengths of 87 cm and 88.5cm respectively, when superimposed, produce 10 beats per second. Find the velocity of sound (Ans : 513.3 m/s)

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Verified answer

wavelength of first sound ,

= 87cm = 0.87m

\lambda_1

wavelength of 2nd sound,

= 88.5cm = 0.885m

\lambda_2

we know,

v=n\lambda

so, frequency is inversely proportional to wavelength.

so, frequency of first ever is higher than frequency of 2nd wave.

given, number of beats per second = 10

so,

n_2-n_1=10

or,

\frac{v}{\lambda_1}-\frac{v}{\lambda_2}=10

or, v(1/0.87 - 1/885) = 10

ANSWER