Question

Word Problem regarding The Doppler Effect?

Answer 1

`320Hz`

Explanation:

Step 1
The problem describes a sound that is moving toward a stationary observer with an air temperature of `15^@C`. Since the speed of sound increases as the temperature increases, we must determine the speed of the waves at `15^@C`. This can be found with the formula:

`color(blue)(|bar(ul(color(white)(a/a)color(black)(v_s=331m/s+((0.6m/s)/(color(white)(i)^@C))xx"temperature")color(white)(a/a)|)))`

Using the formula, the speed of the sound waves is:

`color(darkorange)(v_s)=331m/s+((0.6m/s)/(color(white)(i)^@C))xx15^@C`

`=color(darkorange)(340m/s)`

Step 2
Since the Doppler effect results in a change in the perceived frequency between the source and the observer, we can use the Dopper Effect formula for sound. The sign in the denominator will be a subtraction sign since the source is moving toward the observer:

`color(blue)(|bar(ul(color(white)(a/a)color(black)(f_d=(v_s/(v_s-v_o))f)color(white)(a/a)|)))`

`ul("where:")`
`f_d=`frequency detected by observer
`v_s=`speed of sound wave
`v_o=`speed of object
`f=`frequency at source

`f_d=((color(darkorange)(340m/s))/(color(darkorange)(340m/s)-25m/s))300.0Hz`

`~~color(green)(|bar(ul(color(white)(a/a)color(black)(320Hz)color(white)(a/a)|)))`

Since the detected frequency is higher than `300.0Hz`, the frequency at the source, we can conclude that our answer is correct.