A tuning fork having a frequency of 312 Hz emits a wave which has a wavelength of 1.10 m. Calculate the velocity of sound

1. Analyze the question

We are given the frequency ($f$) of a tuning fork and the wavelength ($\lambda$) of the sound wave it produces. We are asked to calculate the velocity ($v$) of the sound wave.

• Frequency ($f$) = 312 Hz
• Wavelength ($\lambda$) = 1.10 m

2. Explain the concept

In wave motion, the relationship between velocity, frequency, and wavelength is defined by the Wave Equation:

Where:

• $v$ is the velocity of the wave (measured in meters per second, ms$^{-1}$)
• $f$ is the frequency (measured in Hertz, Hz)
• $\lambda$ (lambda) is the wavelength (measured in meters, m)

This formula tells us that the speed of a wave is simply the product of how many waves pass a point per second and the length of each individual wave.

3. Show the solution

Using the wave equation:

Substitute the given values into the formula:

Perform the multiplication:

4. Identify the answer

Comparing our result to the given options: A. 312.0 ms$^{-1}$ B. 110.0 ms$^{-1}$ C. 343.2 ms$^{-1}$ D. 686.4 ms$^{-1}$

The calculated value matches option C.

5. Tip

When solving wave problems in JAMB, always check your units first. If the frequency is in Hz and the wavelength is in meters, your velocity will automatically be in ms$^{-1}$. If the wavelength were given in centimeters, you would need to convert it to meters (divide by 100) before multiplying!