A guitar emits a 440 Hz tone. How far apart are the crests in room temperature air (20 °C)? How long does it take the string to vibrate from crest position to trough position (across twice the amplitude)?
To answer your question, we need two pieces of understanding first.
1. Sound is a wave and the term 'Hz' (Hertz) measures the frequency of those waves (how many waves occur per second). A 440 Hz tone means that the source (the guitar string in this case) is vibrating 440 times per second (440 oscillations/second).
2. The distance between crests (the highest point of a wave) is called the wavelength.
Distance between crests:
The formula to find the wavelength is velocity = frequency * wavelength, where velocity is the speed of sound in air. At a room temperature of 20°C, the speed of sound in air is about 343 m/s. We want to find the distance between crests, the wavelength. Doing the rearrangement of the formula we get: wavelength = velocity/frequency = 343 m/s / 440 Hz = 0.78 meters (approximately).
Time it takes for the string to vibrate from crest position to trough (across twice amplitude):
When a guitar string is played, it vibrates back and forth. Starting from the top (crest), it moves down to the bottom (trough) and back. This back-and-forth motion creates 1 complete wave or cycle. Thus, since the frequency tells us how many cycles occur in one second, finding how long it takes to complete one cycle will involve taking the reciprocal of the frequency. So, the time it takes for one cycle is 1 / 440 Hz = 0.00227 seconds (approximately).
Let me know if you need additional help understanding this!
Explanation:
The weight of the two blocks acts downwards.
Let the weight of the two blocks be W. Solving for T₁ and T₂:
w = T₁/cos 60° -----(1);
w = T₂/cos 30° ----(2);
equating (1) and (2)
T₁/cos 60° = T₂/cos 30°;
T₁ cos 30° = T₂ cos 60°;
T₂/T₁ = cos 30°/cos 60°;
T₂/T₁ =1.73.
Therefore, option a is false since T₂ > T₁.
Option B is true since T₁ cos 30° = T₂ cos 60°.
Option C is true because the T₃ is due to the weight of the two blocks while T₄ is only due to one block.
Option D is wrong because T₁ + T₂ > T₃ by simple summation of the two forces, except by vector addition.
D. Heat each cube to the same temperature, place each cube into different containers with 500 grams of water at the same temperature, and measure the temperature of the water.
The change in temperature is 9.52°CExplanation:Since, the heat supplied by the electric kettle is totally used to increase the temperature of the water.Thus, from the law of conservation of energy can be stated as:Heat Supplied by Electric Kettle = Heat Absorbed by WaterHeat Supplied by Electric Kettle = m C ΔTwhere,Heat Supplied by Electric Kettle = 20,000 JMass of water = m = 0.5 kgSpecific Heat Capacity of Water = C = 4200 J/kg.°CChange in Temperature of Water = ΔTTherefore,20,000 J = (0.5 kg)(4200 J/kg.°C) ΔTΔT = 20,000 J/(2100 J/°C)ΔT = 9.52°C
Weight of barbell (m) = 100 kg
Uplifted to height (h) = 2m
Time taken= 1.5 s
Work done by Jordan = potential energy stored in barbell = mgh
= 100×2×9.8
= 1960J
Power = energy/time
= 1960/1.5
1306.67watts
Weight of jasmine (m) = 400 N
Height climbed on wall (h) = 5m
Total time taken in climbing = 5 sec
Work done in climbing the wall = rise in potential energy = mgh
= 400×9.8×51
= 19600J
Power generated by Jasmine = potential energy / time
= 19600/5
= 3920Watts
Initial velocity (u) = 0
Time taken = 4.5 seconds
Gravitational acceleration (g) = 9.8m/s^2
By the second equation of motion under gravity,
The distance that object fell down (h)
h = ut + (1/2)gt^2
h = 0×4.5 + (1/2)×9.8×(4.5)^2
h = 99.225 m
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