The speed of a transverse wave on a string is 450 m/s, while the wavelength is 0.18 m. The amplitude of the wave is 2.0 mm.
What is the total up and down distance moved by the wave-particle for each cycle of the wave?
What is the frequency of the wave?
What is the period of motion of the wave?
How many cycles of the wave would have to pass by a given point so that a particle on the string moves a total distance of 1.0 km?
How much time is required for a particle on a string to move through a total distance of 1.0 km?
Im suck on the first part of the questions. just help please
To find the total up and down distance moved by the wave-particle for each cycle of the wave, we can simply double the amplitude. The amplitude of the wave is given as 2.0 mm, so the total up and down distance moved by the wave-particle for each cycle is 2 * 2.0 mm = 4.0 mm.
To find the frequency of the wave, we use the formula: Frequency = Speed / Wavelength. The speed of the wave is given as 450 m/s and the wavelength is given as 0.18 m. Plugging these values into the formula gives: Frequency = 450 m/s / 0.18 m = 2500 Hz.
To find the period of motion of the wave, we use the formula: Period = 1 / Frequency. From the previous calculation, we found that the frequency is 2500 Hz, so the period is 1 / 2500 Hz = 0.0004 s.
To find how many cycles of the wave would have to pass by a given point so that a particle on the string moves a total distance of 1.0 km, we divide the total distance by the wavelength. The total distance is given as 1.0 km, which is equal to 1000 m. The wavelength is given as 0.18 m. Plugging these values into the formula gives: Number of cycles = 1000 m / 0.18 m = 5555.6 cycles. Since we can't have a fraction of a cycle, the particle needs to pass by approximately 5556 cycles of the wave.
To find how much time is required for a particle on a string to move through a total distance of 1.0 km, we use the formula: Time = Distance / Speed. The distance is given as 1.0 km, which is equal to 1000 m, and the speed is given as 450 m/s. Plugging these values into the formula gives: Time = 1000 m / 450 m/s = 2.22 s.
To find the total up and down distance moved by the wave-particle for each cycle of the wave, we can use the amplitude of the wave. The amplitude represents the maximum displacement from the equilibrium position.
The total up and down distance moved by the wave-particle for each cycle is twice the amplitude. In this case, the amplitude is given as 2.0 mm (millimeters), so the total up and down distance moved would be:
Total distance = 2 × amplitude
Total distance = 2 × 2.0 mm
Total distance = 4.0 mm
Next, to find the frequency of the wave, we can use the formula:
Frequency (f) = Speed of wave (v) / Wavelength (λ)
In this case, the speed of the wave is given as 450 m/s and the wavelength is given as 0.18 m. Substituting these values into the formula, we get:
Frequency (f) = 450 m/s / 0.18 m
Frequency (f) ≈ 2500 Hz (rounded to the nearest integer)
The frequency of the wave is approximately 2500 Hz.
To find the period of motion of the wave, we can use the formula:
Period (T) = 1 / Frequency (f)
Using the frequency calculated above, we have:
Period (T) = 1 / 2500 Hz
Period (T) ≈ 0.0004 s (rounded to four decimal places)
The period of motion of the wave is approximately 0.0004 seconds.
To determine how many cycles of the wave would have to pass by a given point so that a particle on the string moves a total distance of 1.0 km, we need to know the wavelength of the wave.
Since the wavelength (λ) is given as 0.18 m, we can calculate the number of cycles by dividing the total distance by the wavelength:
Number of cycles = Total distance / Wavelength
Number of cycles = 1000 m / (0.18 m)
Number of cycles ≈ 5556 (rounded to the nearest whole number)
Thus, approximately 5556 cycles of the wave would have to pass by a given point for a particle on the string to move a total distance of 1.0 km.
To find out the time required for a particle on a string to move a total distance of 1.0 km, we can use the relationship:
Speed (v) = Distance (d) / Time (t)
In this case, the speed of the wave is given as 450 m/s and the distance is given as 1000 m. Rearranging the formula, we can solve for time:
Time (t) = Distance (d) / Speed (v)
Time (t) = 1000 m / 450 m/s
Time (t) ≈ 2.22 s (rounded to two decimal places)
Therefore, it would take approximately 2.22 seconds for a particle on a string to move through a total distance of 1.0 km.