18. Waves & Sound

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.

(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 (b) 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 (d) wave velocity (magnitude and direction),.

(II) Consider the point x = 1.00 m on the cord of Example 15–6. Determine (a) 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.

(a) Write an expression for a wave with the same amplitude, wavelength, and frequency but traveling in the opposite direction.

(III) A transverse wave on a cord is given by D( x, t) = 0.12 sin (3.0x - 15.0t) , where D and x are in meters and t is in seconds.

(b) At t = 0.20s, what are the displacement, velocity, and acceleration of a point on the cord where x = 0.60m?

(II) A transverse wave with a frequency of 220 Hz and a wavelength of 10.0 cm is traveling along a cord. The maximum speed of particles on the cord is 0.10 the wave speed. What is the amplitude of the wave?

(II) A transverse wave pulse travels to the right along a string with a speed v = 2.0 m/s. At the shape of the pulse is given by the function D = 0.45 cos (2.6x + 1.2),

where D and x are in meters. (b) Determine a formula for the wave pulse at any time t assuming there are no frictional losses.

Figure 15–44 shows the wave shape at two instants of time for a sinusoidal wave traveling to the right. What is the mathematical representation of this wave?

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