Question

1.2 A wave is represented by the equation y = 2sin (0.5x – 200t), when all distances are measured in centimeters and time in seconds. For this wave, calculate its
1.2.1 Frequency [4 marks]
1.2.2 Wavelength [4 marks]
12.3 speed [4marks]

Answer 1

Answer:

Frequency of the wave  = 100 Hz

Wavelength of the wave = 4 cm

Speed of the wave = 4 m/s

Explanation:

The general equation of the wave is

$\boxed{y=A\sin\frac{2\pi}{\lambda} (ut-x)}$

or, $\boxed{y=A\sin2\pi(ft-\frac{x}{\lambda})}$

Where A is amplitude, f is frequency and λ is wavelength

The given equation of the wave is

$y = 2\sin\pi (0.5x-200t)$

or, $y = 2\sin2\pi (\frac{x}{4} -100t)$

or, $y = -2\sin2\pi (100t-\frac{x}{4})$

Comparing this equation with the general wave equation

We get

Amplitude A = 2 cm

Wavelength λ = 4 cm

Frequency f = 100 Hz

Speed of the wave = fλ = 100 × 4 cm/s

                                       = 400 cm/s

                                       = 4 m/s

Hope this helps.