The frequency of sinusodial wave y = 0.40cos [2000 t + 0.80] would be
- $1000\, \pi \,Hz$
- $2000 \,Hz$
- $20\, Hz$
- $\frac{1000}{\pi} \,Hz$
The Correct Option is D
Solution and Explanation
To determine the frequency of the given sinusoidal wave represented by the equation \( y = 0.40\cos(2000t + 0.80) \), we can use the standard form of a sinusoidal function:
y = A\cos(\omega t + \phi)
where:
- A is the amplitude,
- \omega is the angular frequency in radians per second,
- t is the time,
- \phi is the phase shift.
In the equation given:
- The amplitude A is 0.40.
- The angular frequency \omega is 2000.
- The phase shift \phi is 0.80 radians.
The relationship between the angular frequency \omega and the frequency f (in Hz) is given by:
\omega = 2\pi f
We can rearrange this equation to solve for the frequency:
f = \frac{\omega}{2\pi}
Substituting the given value of \omega = 2000:
f = \frac{2000}{2\pi} = \frac{1000}{\pi}
Therefore, the frequency of the sinusoidal wave is \frac{1000}{\pi} \, \text{Hz}.
Thus, the correct option is \frac{1000}{\pi} \, \text{Hz}.
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Concepts Used:
Waves
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
- Water waves (ripples of gravity waves, not sound through water)
- Light waves
- S-wave earthquake waves
- Stringed instruments
- Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
Examples of longitudinal waves:
- Sound waves
- P-type earthquake waves
- Compression wave