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Doppler Effect and Speed Along a String

Sound 3D longitudinal waves Sound waves that can be heard – Audible – 20-20,000 Hz.

Sound Waves Sound waves that are below 20Hz are called infrasonic – Ground Waves Sound waves above 20,000 Hz are called ultrasonic – Dog whistles – Baby Pictures

Doppler Effect Big Bang Style

Doppler Effect As the object moves toward the observer, the speed of the waves are the speed of sound plus the speed of the object, therefore the waves are “crunched” together. – Pitch increases

Doppler Effect

Works for objects moving away from listener.

Doppler Effect Apparent Frequency – Away from observer f’ = f o (Speed of sound/(speed of sound + v source )) Negative velocity means the object is moving towards the observer

Doppler Effect This also works when the observer is moving.

Doppler Effect Observer moving – f’ = f o ((speed of sound + v)/speed of sound) V is negative when moving away from the object Both observer and object moving – f’ = f o ((S+v observer )/(S + v source ))

Question I On a standard day, the speed of sound is 345m/s. A whistle whose frequency is 1000Hz is moving toward an observer at a speed of 52.0m/s. What is the frequency of the sound heard by the observer?

Answer 1180Hz

Question II A train moving at a speed of 50m/s sounds its whistle, which has a frequency of 620Hz. The speed of sound on this particular day is 335m/s. Determine the frequency heard by the stationary observer A) as the train approaches and B) as the train moves away.

Answer 730Hz and 540Hz

Question III On a standard day, the speed of sound is 345m/s. An observer is moving at a speed of 35m/s away from a whistle whose frequency is 1000Hz. What is the observed frequency of the whistle?

Answer 898Hz

Works for Light

What about a duck????

Speed Along a String

Tension created by the hanging mass affects the speed of the wave. The linear density of the string also affects the speed. – It is the mass of the string divided by the length

Speed Along a String

Example IV A uniform string has a mass of 0.40kg and a length of 5.0m. The tension in the string is provided by a 3.0kgmass. Find the speed of a pulse in this string.

Answer 19m/s.

Sound Intensity Intensity – Intensity = Power/Surface Area (W/m 2 ) Alexander Graham Bell –Logarithmic scale decibels dB

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Example V A mass is used to provide tension in the string. The speed of the pulse traveling along the string is v. By what factor should the mass be multiplied in order for the pulse to have a speed of 3v?

Answer 9 times greater mass