Answer to Question #218925 in Classical Mechanics for Bob

Question

1) A pendulum has a mass of 2.35 kg. If the pendulum swings back and forth 110 times in 90.0 seconds, what is the length of the pendulum?

2) A vertical spring is stretched 60.0 cm by a hanging 5.00 kg mass.

a. What is the spring constant?

b. What will be the frequency of vibration of this spring system?

3) Radio telescopes receive waves from distant stars. If such a wave has a wavelength of 24 cm and travels at the speed of light (c = 3.00 x 10 8 m/s), what is the frequency?

4) The speed and wavelength of coastal water waves are 4.0 m/s and 6.0 m respectively. When the waves enter a shallower region, the speed decreases to 1.7 m/s. What is the wavelength in the shallower region?

5) The first resonant length of a closed air column occurs when the length is 40 cm. What will the third resonant length be?

6) A police car with a siren that has a frequency of 900 Hz is moving toward you at 32.0 m/s. Given that the speed of sound is 340 m/s, what is the apparent frequency you hear?

Answer 1

1)

$$\frac{90}{110}=2\pi\sqrt{\frac{l}{9.8}}\\l=0.166\ m$$

2)

$$5(9.8)=0.6k\\k=81.7\frac{N}{m}$$

$$\frac{1}{f}=2\pi\sqrt{\frac{5}{81.7}}\\f=0.643\ Hz$$

3)

$$f=\frac{3\cdot10^8}{0.24}=1.25\cdot10^9Hz$$

4)

$$\frac{4}{6}=\frac{1.7}{\lambda}\\\lambda=2.55\ m$$

5)

$$\lambda=\frac{5}{4}40=50\ cm$$

6)

$$f=\frac{340}{340-32}900=994\ Hz$$