Questions: A 708.1 Hz sound has a velocity of 1084 ft / s in the air and a velocity of 4992.9 ft / s in water. Find the wavelength of this sound in (a) air and ft (b) the water. ft

Solution Steps

We are given:

• Frequency of the sound, \( f = 708.1 \) Hz
• Velocity of sound in air, \( v_{\text{air}} = 1084 \) ft/s
• Velocity of sound in water, \( v_{\text{water}} = 4992.9 \) ft/s

The wavelength \( \lambda \) can be calculated using the formula: \[ \lambda = \frac{v}{f} \] where \( v \) is the velocity of sound and \( f \) is the frequency.

For air: \[ \lambda_{\text{air}} = \frac{v_{\text{air}}}{f} = \frac{1084 \, \text{ft/s}}{708.1 \, \text{Hz}} \]

For water: \[ \lambda_{\text{water}} = \frac{v_{\text{water}}}{f} = \frac{4992.9 \, \text{ft/s}}{708.1 \, \text{Hz}} \]

For air: \[ \lambda_{\text{air}} = \frac{1084}{708.1} \approx 1.530 \, \text{ft} \]

For water: \[ \lambda_{\text{water}} = \frac{4992.9}{708.1} \approx 7.050 \, \text{ft} \]

Final Answer