Intro to Waves

A satellite captures images of a tsunami, and properties of the tsunami can be found from these images, providing important information to people who need to evacuate coastal areas. If satellite images of a tsunami show the distance from one peak to another is 500 km, and the period is 1 hour, how much time do people have to evacuate if the tsunami is found to be 100 km off shore?

Write the mathematical representation of the wave graphed in the following two figures.

A transverse wave is represented by the following function:y = (18 cm) sin [2π (x/2cm) − t/5s + 1/4)]. What is the phase angle of this wave?

The function for some transverse wave is ? = (0.5 m) sin [(0.8 m⁻¹)x − 2?(50 Hz)t + π/3]. What is the transverse velocity at t=2 s, x=7 cm? What is the maximum transverse speed? The maximum transverse acceleration?

A 2 m long string is arranged as shown in the figure below. If the mass of the string is 0.5 kg, what would the frequency be of a wave with a 2 cm wavelength?

In the following figure, two interfering waves are drawn at some instance in time. 

a. Indicate the regions on the graph where constructive interference occurs.
b.Indicate the regions on the graph where destructive interference occurs.

In the following figure, what is the harmonic number of the standing wave? The wavelength of the standing wave? If the frequency of the standing wave is 30 Hz, what is the speed of the waves producing the standing wave?

An unknown mass hangs on the end of a 2 m rope anchored to the ceiling when a strong wind causes the rope to vibrate and hum at its fundamental frequency of 100 Hz. If the rope has a mass of 0.15 kg, what is the unknown mass?

A sound wave is emitted at a frequency of 300 Hz in air at a 0°C. As the sound wave travels through the air, the temperature increases. What is the wavelength of the sound wave at the following temperatures?

a. 0°C
b. 20°C
c. 45°C

A source emits a sound in the shape of a cone, as shown in the figure below. If you measure the intensity to be 100 W/m² at a distance of 0.5 m, what is the power of the source?

A source emits sound spherically with a power of 2.2 × 10⁴ W. What is the minimum distance away from this sound that would be considered safe (a volume of 150 dB or less)?

A police siren emits a sound somewhere around 700 Hz. If you are waiting at a red light, and a police car approaches you from behind and passes you, moving at a constant 30 m/s, what is the frequency you hear from the siren as it approaches you from behind? What about once it’s passed you? Assume the air temperature to be 20°C.

A string emits an unknown sound. You strike a tuning fork which emits a sound at EXACTLY 300 Hz, and you hear a beat frequency of 20 Hz. You then tighten the string, increasing the tension in string. After you pluck the string and strike the tuning fork, you hear a new beat frequency of 30 Hz. What is the unknown frequency of the string, originally?