Question

Two tuning forks of frequencies 320 Hz and 340 Hz are sounded together to produce sound waves. The velocity of sound in air is 326.4 m/s. Calculate the difference in wavelengths of these waves.

Hint:

The difference in wavelengths of two sound waves is inversely proportional to the difference in their frequencies, given that the velocity of sound remains constant.

Answer 1

Step 1: Formula for wavelength.
The wavelength \( \lambda \) of a sound wave is given by the formula: \[ \lambda = \frac{v}{f} \] where \( v \) is the velocity of sound and \( f \) is the frequency.
Step 2: Calculate wavelengths.
For the first tuning fork with a frequency of 320 Hz: \[ \lambda_1 = \frac{v}{f_1} = \frac{326.4}{320} = 1.02 \, \text{m} \] For the second tuning fork with a frequency of 340 Hz: \[ \lambda_2 = \frac{v}{f_2} = \frac{326.4}{340} = 0.96 \, \text{m} \]
Step 3: Difference in wavelengths.
The difference in wavelengths is: \[ \Delta \lambda = \lambda_1
- \lambda_2 = 1.02
- 0.96 = 0.06 \, \text{m} \]