Question

a sound wave traveling through dry air has a frequency of 16 hz, a wavelength of 22 m, and a speed of 350 m/s. when the sound wave passes through a cloud of methane, its wavelength changes to 28 m, while its frequency remains the same. what is its new speed? (the equation for the speed of a wave is ( v = f\timeslambda ).)
a. 350 m/s
b. 13 m/s
c. 9,800 m/s
d. 448 m/s

Explanation:

Step1: Identify the formula

The formula for the speed of a wave is \(v = f\times\lambda\).

Step2: Determine the frequency

Given \(v = 350\space m/s\) and \(\lambda=22\space m\) in dry air. Using \(v = f\times\lambda\), we can find \(f=\frac{v}{\lambda}\). But since frequency \(f\) remains the same in methane, we can also directly use the new \(\lambda = 28\space m\) and the original \(f\).
Since \(f = 16\space Hz\) (given in the problem, we can also check \(f=\frac{350}{22}\approx16\space Hz\) from the first - medium data, but the problem states \(f = 16\space Hz\) remains constant).

Step3: Calculate the new speed

Substitute \(f = 16\space Hz\) and \(\lambda=28\space m\) into \(v = f\times\lambda\). So \(v=16\times28\).

$$v = 16\times28=(10 + 6)\times28=10\times28+6\times28=280+168 = 448\space m/s$$

Answer:

D. \(448\space m/s\)