Question

xample 8.1: The speed of sound in air is 330
Vms and that in glass is 4500 m/s. What is the
ratio of the wavelength of sound of a given
frequency in the two media?
Solution:
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Answer 1

Answer:

wavelength= speed÷frequency

ratio of wavelength= 330÷4500

=11÷150

11:150

ratio of frequency= 150:11

Answer 2

Answer:

the ratio of the wavelength of sound in two media is 0.073.

Explanation:

Given : speed of sound in air = 330m/s

          : speed of sound in glass = 4500m/s

We have a relation between the wavelength, frequency, and speed given by the following expression

         $v= \nu \times \lambda$

   $v= velocity\ \ of\ \ wave \\\nu = frequency\ \ of \ \ given \ \wave \\\lambda= wavelength \ \of \ \given \ \wave$

we have to find the ratio of the wavelength of sound in two given media

frequency is the same so,

   $v_{air} = \lambda _{air} \times \nu\\\\v_{glass}= \lambda _{glass} \times \nu\\\\\frac{v_{air} }{v_{glass}} =\frac{ \lambda _{air} \times \nu }{ \lambda _{glass} \times \nu } \\\\\frac{330}{4500} =\frac{ \lambda _{air} }{ \lambda _{glass}} \\\\0.073 =\frac{ \lambda _{air} }{ \lambda _{glass}}\\\\ \frac{ \lambda _{air} }{ \lambda _{glass}}= 0.073$

Hence the ratio of the wavelength of sound in the two media is 0.073.