# Fundamental frequency and wavelength, speed of a wave

A steel piano string is .05m in length, with a mass of .005kg, and has a tension of 400N.

1) what is the fundamental frequency and wavelength of the string?

2) What is the speed of a wave on this string?

3) If the tension is increased to 450N, what is the new fundamental frequency?

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#### Solution Summary

The solutions shows all the formulas used in solving the problem.

Frequency of sound, siren intensity, guitar string, wavelength

1. Suppose you place a speaker in front the open end of a tube which is closed at the other end, and vary the frequency of a pure sound (sine wave) produced by the speaker. You find that there are resonances at 300 Hz and 500 Hz, among many others.

(A) resonance is a frequency at which the sound in the tube is very loud because there is a standing wave, which builds up in intensity.) We should also note that there are no resonances between 300 Hz and 500 Hz. (A) Determine the length of the tube. Provide a narrative of how you approach this problem, and show the node/antinode patterns for the 300 Hz and 500 Hz resonances. Assume the speed of sound in air is 343 m/s.

(B) What is the fundamental (lowest) frequency supported by the tube? Show your reasoning clearly, preferably with a diagram or two.

2. A siren on top of a tower produces a sound whose power level is measured to be 68 dB at a distance 50 m from the tower.

(A) Determine the intensity (in W/m2) at that position.

(B) Determine the sound power level, in dB, at a position 150 m from the tower. Assume that the 1/r2 law is obeyed by the intensity of the sound. (You will first have to determine the intensity in W/m2.)

3. A certain guitar string is 0.80 m long and vibrates at 180 Hz in its fundamental (lowest frequency) mode.

(A) Find the speed of the wave along the string.

(B) Suppose the total mass of the string is 10.0 grams. What then is the mass per unit length of the string? Find the tension in the guitar string. (Be careful to use SI units!)

4. What is the period, in m/s of a sound whose frequency is 9800 Hz?

5. The wavelength of green light is 550 nm and the speed of light in a vacuum is 3.00×108 m/s. What is the frequency of 550-nm light? (Answer: 5.45×1014 Hz)

6. You will need a whole page of graph paper for this one. Sketch a graph of a sine wave. Take up the entire width of the paper, displaying 2 complete cycles. The height of the wave should be 1 to 1.5 inches, as you wish. Now, on the same graph but using a dashed line, sketch another sine wave with the same frequency, but out of phase by 90°: the second wave should lag the first by 90°. (This means, for example, that a "zero" of the second wave occurs when the first wave has a value of 1.0.) Finally, sketch the sum of the two waves. (Use a different color or a heavier pen to tell the difference.) You don't have to do any arithmetic. Just add the vertical distances visually for several points and draw a smooth curve through your points.

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