Question

A sound wave has a frequency of $192Hz$ and travels the length of a football field, $91.4m$, in $0.27s$. If the frequency was changed to $442Hz$, what would be the new wavelength?

• A. $0.76m$
• B. $1.25m$
• C. $0.56m$
• D. $7.6m$

Answer 1

The correct option is A $0.76m$

Given the frequency, distance traveled and the time taken, the wavelength of the sound wave cannot be directly calculated. The speed of the sound wave is first derived and then with the speed we can calculate the wavelength with that value.

The speed of the sound, distance traveled and the time taken relationship is given as follows.

$Speedofsound=\frac{Distancetraveled\left(m\right)}{Timetaken\left(s\right)}$.

In the question it is given that distance traveled is 91.4 m (length of the football field) and the time taken 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 $Wavelength,\lambda =\frac{Speed,v}{Frequency,\nu }$,

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 is changed from 192 Hz to 442 Hz and the speed is 338.5 m/s(from the above calculation - it remains the same).

That is, $\lambda =\frac{v}{\nu }=\frac{338.5m/s}{442Hz}=0.76m$

Hence, the changed wavelength of the sound wave is 0.76 meters.