Question

the speed of sound in dry air at 20°c is 343.5 m s^-1, and the frequency of the sound from the note c above middle c on the piano is 523.2 s^-1 (according to the american standard pitch scale). calculate the wavelength of the sound and the time it will take to travel 28.3 m across a concert hall.
wavelength =
time =
use the references to access important values if needed for this question.

Explanation:

Step1: Calculate the wavelength

The formula for the wavelength $\lambda$ of a sound wave is $\lambda=\frac{v}{f}$, where $v$ is the speed of sound and $f$ is the frequency.
Given $v = 343.5\ m/s$ and $f=523.2\ s^{-1}$
$\lambda=\frac{343.5}{523.2}\approx0.6566\ m$

Step2: Calculate the time

The formula for time $t$ is $t = \frac{d}{v}$, where $d$ is the distance and $v$ is the speed of sound.
Given $d = 28.3\ m$ and $v = 343.5\ m/s$
$t=\frac{28.3}{343.5}\approx0.0824\ s$

Answer:

Wavelength = $0.657\ m$ (rounded to three decimal places)
Time = $0.0824\ s$