Question

a stereo speaker produces a pure \e\ tone, with a frequency of 329.6 hz.
what is the period ( t ) of the sound wave produced by the speaker?
( t=)
what is the wavelength ( lambda_{\text {water }} ) of the same sound wave as it enters some water, where it has a speed of about 1480 m/s?
( lambda_{\text {water }}=)
what is the wavelength ( lambda_{\text {air }} ) of this sound wave as it travels through air with a speed of about 341 m/s?
( lambda_{\text {air }}=)

Explanation:

Step1: Calculate the period \( T \)

The relationship between frequency \( f \) and period \( T \) is \( T=\frac{1}{f} \). Given \( f = 329.6\ Hz \), then \( T=\frac{1}{329.6}\ s\approx0.00303\ s \).

Step2: Calculate the wavelength in water \( \lambda_{water} \)

The wave - speed formula is \( v = f\lambda \), so \( \lambda=\frac{v}{f} \). Given \( v_{water}=1480\ m/s \) and \( f = 329.6\ Hz \), then \( \lambda_{water}=\frac{1480}{329.6}\ m\approx4.49\ m \).

Step3: Calculate the wavelength in air \( \lambda_{air} \)

Using \( \lambda=\frac{v}{f} \) again, with \( v_{air}=341\ m/s \) and \( f = 329.6\ Hz \), then \( \lambda_{air}=\frac{341}{329.6}\ m\approx1.03\ m \).

Answer:

\( T = 0.00303\ s \)
\( \lambda_{water}=4.49\ m \)
\( \lambda_{air}=1.03\ m \)