Question

What is the frequency of a wave with a speed of \(30\,m/s\) if the distance between 11 consecutive crests is \(1\,m\)?

• A. \(30\,Hz\)
• B. \(300\,Hz\)
• C. \(330\,Hz\)
• D. \(3\,Hz\)

Hint:

If \(n\) consecutive crests are given, the number of wavelengths between them is \(n-1\). Use this to determine the wavelength before applying \(v = f\lambda\).

Answer 1

The Correct Option is B

Concept: Wave motion is described by the relation between wave speed, wavelength, and frequency: \[ v = f\lambda \] where \(v\) = wave speed, \(f\) = frequency, \(\lambda\) = wavelength. The wavelength is the distance between two successive crests or troughs of a wave.

Step 1: Determine the number of wavelengths.
If there are 11 consecutive crests, the number of intervals between them is one less than the number of crests. \[ \text{Number of wavelengths} = 11 - 1 = 10 \] Thus, \[ 10\lambda = 1\,m \]

Step 2: Calculate the wavelength.
\[ \lambda = \frac{1}{10} \] \[ \lambda = 0.1\,m \]

Step 3: Use the wave speed formula.
\[ v = f\lambda \] \[ f = \frac{v}{\lambda} \]

Step 4: Substitute the given values.
\[ f = \frac{30}{0.1} \] \[ f = 300\,Hz \]

Step 5: Final result.
\[ \boxed{300\,Hz} \]