Word Problem regarding The Doppler Effect?

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1 Answer
Jun 29, 2016

Answer:

#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.