If you wait at a railroad crossing as a train approaches and passes, you hear a Doppler shift in its sound. But if you listen closely, you hear that the change in frequency is continuous; it does not suddenly go from one high frequency to another low frequency. Instead the frequency smoothly (but rather quickly) changes from high to low as the train passes. Why does this smooth change occur?

The A-string on a guitar is 0.648 m long and has a linear mass density of 4.25 g/m. If the string is perfectly in tune, then the third harmonic should have a frequency of 330 Hz. However, on a particular out-of-tune guitar, the A-string's third harmonic is measured to be 319 Hz. By how much should the tension be increased in order to bring the A-string back into tune? (You may ignore any slight changes to the linear mass density of the string that might result from the tuning process.)

A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and whirling it around her head in a horizontal circle at 1100 rpm. What are the highest and lowest frequencies heard by a student in the classroom?

The pan flute is a musical instrument consisting of a number of closed-end tubes of different lengths. When the musician blows over the open ends, each tube plays a different note. The longest pipe is 0.33 m long. What is the frequency of the note it plays?

The auditory canal of the outer ear acts as a closed end resonator which has a natural frequency of around 3500 Hz. This canal serves to amplify sounds with frequencies around this value, thus making us more sensitive to such frequencies. If the speed of waves inside the canal is 350 m/s, then what is the estimated length of the canal?

A train is moving away from an observer at a speed of 50 m/s with its whistle on, the frequency of the whistling sound being 400 Hz. What should be the approximate frequency heard by a stationary observer? Take the speed of sound as 345 m/s when atmospheric temperature is 24°C. 328 Hz 310 Hz 380 Hz 349 Hz

Two identical piano strings of length 0.750 m are each tuned exactly to 440 Hz. The tension in one of the strings is then increased by 1.0%. If they are now struck, what is the beat frequency between the fundamentals of the two strings?

Two pianos each sound the same note simultaneously, but they are both out of tune. On a day when the speed of sound is 341 m/s, piano A produces a wavelength of 0.763 m, while piano B produces a wavelength of 0.780 m. How much time separates successive beats?

If the vocal tract of a human is considered a closed tube 17 cm in length, what is the frequency of what would become the second harmonic? Consider 340 m/s as the speed of sound. The answer must be in Hz units.

Two strings both vibrate at exactly 802 Hz. The tension in one of them is then increased slightly. As a result, 3 beats per second are heard when both strings vibrate. What is the new frequency of the string that was tightened?  Calculate to one decimal.