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musickatia [10]
2 years ago
6

When the C4 key on a piano keyboard is pressed, a string inside the piano is struck by a hammer and begins vibrating back and fo

rth at approximately 260 cycles per second.
a. What is the frequency in Hertz of the sound wave?
b. What is the wavelength of the wave?
Physics
1 answer:
Anettt [7]2 years ago
8 0

Answer:

Frequency = 260 Hz and wavelength = 1.31 m

Explanation:

Given that,

A hammer begins vibrating back and forth at approximately 260 cycles per second.

(a) The frequency of an object is the number of vibrations per unit time. The frequency of the sound wave is 260 Hz.

(b) The speed of sound in air is 343 m/s. So,

v=f\lambda\\\\\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{343}{260}\\\\\lambda=1.31\ m

Hence, this is the required solution.

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The length of a simple pendulum is 0.81 mand the mass of the particle (the "bob") at the end of the cable is0.23 kg. The pendulu
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Answer:

\displaystyle w=3.478\ rad/sec

M=0.0182\ J

v=0.398\ m/s

Explanation:

<u>Simple Pendulum</u>

It's a simple device constructed with a mass (bob) tied to the end of an inextensible rope of length L and let swing back and forth at small angles. The movement is referred to as Simple Harmonic Motion (SHM).

(a) The angular frequency of the motion is computed as

\displaystyle w=\sqrt{\frac{g}{L}}

We have the length of the pendulum is L=0.81 meters, then we have

\displaystyle w=\sqrt{\frac{9.8}{0.81}}

\displaystyle w=3.478\ rad/sec

(b) The total mechanical energy is computed as the sum of the kinetic energy K and the potential energy U. At its highest point, the kinetic energy is zero, so the mechanical energy is pure potential energy, which is computed as

U=mgh

where h is measured to the reference level (the lowest point). Please check the figure below, to see the desired height is denoted as Y. We know that

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H=L\ cos\alpha

Solving for Y

Y=L(1-cos\alpha )

Since\ \alpha=8.1^o, L=0.81\ m

Y=0.0081\ m

The potential energy is

U=mgh=0.23\ kg(9.8\ m/s^2)(0.0081\ m)

U=0.0182\ J

The mechanical energy is, then

M=K+U=0+U=U

M=0.0182\ J

(c) The maximum speed is achieved when it passes through the lowest point (the reference for h=0), so the mechanical energy becomes all kinetic energy (K). We know

\displaystyle K=\frac{mv^2}{2}

Equating to the mechanical energy of the system (M)

\displaystyle \frac{mv^2}{2}=0.0182

Solving for v

\displaystyle v=\sqrt{\frac{(2)(0.0182)}{0.23}}

v=0.398\ m/s

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