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Question
Two tuning forks having frequencies 320 Hz and 340 Hz are sounded together to produce sound waves. The velocity of sound in air is 340 m/s. Find the difference in wavelength of these waves.
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Solution
Given:
- n1 = 320 Hz
- n2 = 340 Hz
- v = 340 m/s
To find:
Difference in wavelength (λ1 − λ2) = ?
Formula:
`lambda_1 = v/n_1 and lambda_2 = v/n_2`
Here, n1 < n2,
∴ λ1 > λ2
∴ `lambda_1 - lambda_2 = 1/n_1 - v/n_2`
∴ `lambda_1 - lambda_2 = v[1/n_1 - v/n_2]`
∴ `lambda_1 - lambda_2 = 340[(340 - 320)/(320 xx 340)]`
∴ `lambda_1 - lambda_2 = 340[20/(320 xx 340)]`
∴ `lambda_1 - lambda_2 = cancel340[20/(320 xx cancel340)]`
∴ `lambda_1 - lambda_2 = 1/16`
∴ `lambda_1 - lambda_2 = 0.0625 m`
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