Waves and Resonance, Physics help?
An elastic cord is 63 cm long when a weight of 52 N hangs from it but is 89 cm long when a weight of 79 N hangs from it. What is the “spring” constant k of this elastic cord?
It takes a force of 80.0 N to compress the spring of a toy popgun 0.193 m to “load” a 0.147 kg ball. With what speed will the ball leave the gun?
(a) At T = 15°C, how long must an open organ pipe be to have a fundamental frequency of 292 Hz?
(b) If this pipe is instead filled with helium at 20°C, what is its fundamental frequency?
A piano tuner hears one beat every 2.8 s when trying to adjust two strings, one of which is sounding 440 Hz, so that they sound the same tone. How far off in frequency is the other string?
You can answer just one, anything will help.
1. 52 = k(0.63 – Xo) 79 = k(0.89- Xo) You have two eqns with 2 unknowns. Eliminate Xo and solve for k.
2. First fine the spring constant: 80 = k(0.193) solve for k.
Then use conservation of energy (1/2)kx^2 = (1/2)mv^2. Solve for v.
3. Open at one end or both ends? One end: 1/4 wavelength in pipe
Both ends: 1/2 wavelength in pipe. Use that fact and v = f * wavelength where v is the velocity of sound at 15C.
4. Only difference is that you will have to use the speed of sound in helium at 20C.
Good luck.
Tuning an organ
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