What is the difference between the number of cycles in the first and the second wave, given that both waves travel an equal horizontal distance in one second?

Question

What is the difference between the number of cycles in the first and the second wave, given that both waves travel an equal horizontal distance in one second?

Answer 1

What’s the answer

Answer 2

To determine the difference between the number of cycles in the first and second wave, we need to understand the concept of frequency and wavelength.

Frequency (f) is the number of cycles or oscillations per second, measured in hertz (Hz).

Wavelength (λ) is the distance between corresponding points on two consecutive waves, such as the distance between two peaks or two troughs.

Given that both waves travel an equal horizontal distance in one second, it implies that their speed is the same, since speed is distance traveled divided by time taken.

Now, let's assume that the first wave has a frequency of f1 and a corresponding wavelength of λ1, while the second wave has a frequency of f2 and a corresponding wavelength of λ2.

Since both waves travel equal distances in one second, their speeds must be the same. Therefore, we can write:

Speed of first wave = Speed of second wave

This can be expressed as:

f1 * λ1 = f2 * λ2

Since the speed of the waves is the same, we can equate the product of frequency and wavelength for both waves.

Now, to find the difference between the number of cycles in the first and second wave, we need to compare their frequencies. So, let's solve the equation above for the frequency ratio:

(f1 / f2) = (λ2 / λ1)

Therefore, the difference between the number of cycles in the first and second wave is determined by the ratio of their wavelengths.

Answer 3

To answer this question, we need to understand the concept of frequency and wavelength in wave motion.

Frequency refers to the number of cycles or oscillations a wave completes in one second. It is typically measured in hertz (Hz). Wavelength, on the other hand, represents the distance between two corresponding points on a wave, such as between two crests or two troughs.

Given that both waves travel an equal horizontal distance in one second, we can assume that their velocities are the same. Consequently, the waves must have the same wavelength.

Now, let's look at the relationship between frequency, wavelength, and velocity. The velocity of a wave can be calculated by multiplying its frequency (f) by its wavelength (λ). Mathematically, this can be expressed as:

Velocity (v) = Frequency (f) x Wavelength (λ)

Since both waves have the same velocity (as they travel the same horizontal distance in one second), and also the same wavelength, we can conclude that their frequencies must be equal as well.

Therefore, the difference between the number of cycles in the first and the second wave is zero since both waves have the same frequency.