Question

A sound wave has a frequency of 192 Hz and travels the length of a football field, 91.4 m, in 0.27 s. What is the wavelength of the wave?

• A. $0.88m$
• B. $1.76m$
• C. $3.52m$
• D. $7.04m$

Answer 1

Answer: (B)

$1.76m$

$Speedofsound=\frac{Distancetraveledinm}{Timetakenins}$.
In the question, it is given that the distance travelled$\left(s\right)$ is 91.4 m (length of the football field) and the time taken$\left(t\right)$ is 0.27 seconds.
The speed of the sound wave is calculated as follows.
$v=\frac{s}{t}=\frac{91.4m}{0.27s}=338.5m/s$
Hence, the speed of the sound wave is 338.5 m/s.
Now the wavelength is calculated from the below relation .
The relationship between the velocity of the sound, its wavelength and frequency is given by the formula $Wavelength\lambda =\frac{Speedv}{Frequency\nu }$,
where,
$v$ - velocity of the wave
$\lambda$- wavelength of the wave
f - frequency of the wave.
In the question it is given that the frequency$\left(\nu \right)$ is 192 Hz and the speed$\left(v\right)$ is 338.5 m/s(from the above calculation).
That is, $\lambda =\frac{v}{\nu }=\frac{338.5m/s}{192Hz}=1.76m$
Hence, the wavelength of the sound wave is 1.76 meters.