18. Waves & Sound

In which type of wave is the disturbance parallel to the direction of wave travel?

If the speed of a wave ($v$) increases while its wavelength ($\lambda$) remains constant, what happens to the wave's frequency ($f$)?

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

A transverse wave is represented by the following function: $y=\left(18\operatorname{cm}\right)\sin\left[2\pi\left(\frac{x}{2\operatorname{cm}}-\frac{t}{5s}+\frac14\right)\right]$. 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 transverse harmonic wave moving to the left has a wavelength of 2.5 m and a wave speed of 12 m/s. The amplitude of the wave is 0.1 m. At x = 0 and t = 0, the displacement of the wave is y = 0. Write the wave function for this wave.

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is $y(x,t)=\left(2.30\operatorname{mm)}\cos[\left(16.98\text{ }rad/m\right)x+(742\text{ }rad/s\right)t]$. Being more practical, you measure the rope to have a length of $1.35\text{ m}$ and a mass of $0.00338\operatorname{kg}$. You are then asked to determine the following: (d) wave speed; (e) direction the wave is traveling;

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is $y(x,t)=\left(2.30\operatorname{mm)}\cos[\left(16.98\text{ }rad/m\right)x+(742\text{ }rad/s\right)t]$. Being more practical, you measure the rope to have a length of $1.35\text{ m}$ and a mass of $0.00338\operatorname{kg}$. You are then asked to determine the following: (a) amplitude; (b) frequency; (c) wavelength.

A sound wave is described by $D(y,t)=\left(0.0200\text{mm}\right)\times \sin \left[\right(8.96\text{rad/m})y+(3140\text{rad/s})t+\pi /4\text{rad}]$, where $y$ is in $m$ and $t$ is in $s$. Along which axis is the air oscillating?

Show that the displacement D(x,t) = cx² + dt², where c and d are constants, is a solution to the wave equation. Then find an expression in terms of c and d for the wave speed.

(II) A transverse traveling wave on a cord is represented by D = 0.22 sin (5.6x + 34 t) where D and x are in meters and t is in seconds. For this wave determine frequency.

(II) A transverse traveling wave on a cord is represented by D = 0.22 sin (5.6x + 34 t) where D and x are in meters and t is in seconds. For this wave determine wave velocity (magnitude and direction).

Consider the point x = 1.00 m on the cord of Example 15–6. Determine the maximum acceleration of this point.

(I) A transverse wave on a wire is given by D (x, t) = 0.015 sin (35x - 1200 t) where D and x are in meters and t is in seconds. Write an expression for a wave with the same amplitude, wavelength, and frequency but traveling in the opposite direction.