Question on Frequencies at different Resonance

Waves and Sounds is one of the basic concept in Physics which deals with wavelength, frequency and velocity of waves and sounds under uniform motion. Initial Frequency generated by any instrument is called as fundamental frequency and sound harmonics.

Topic : Vibrating String with a property of Resonance

Resonance is the tendency of an instrument to vibrate with large amplitude.

Question : A particular string resonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonate.

Solution :

Four loops means four anti-nodes, which means that we have the fourth harmonic, as the fundamental is one "loop" or anti-node.

The fourth harmonic would be four times the fundamental, so therefore the fundamental is 280 Hz/4 = 70 Hz,

and the next two would be 140 Hz, and 210 Hz.

So f₁ = 70Hz (fundamental frequency)
f₂ = 2f₁ = 2 x 70 = 140 Hz
f₃ = 3f₁ = 3 x 70 = 210 Hz
f₄ = 4f₁ = 4 x 70 = 280 Hz

For more explanations related to the concept can be found in physics help or science help.

Question to Determine Velocity of Rollar Coaster

Roller coaster’s motion is a type of motion. Here is a word problem to determine the velocity of moving roller coaster. Balanced or unbalanced forces when applied on any body there occur a motion and the speed at which the body moves is velocity of that body.

Topic : Velocity of Moving Body

Since Potential Energy is equal to Kinetic energy in the system, m*g*h = 1/2*m*v² is the formula to find velocity of a body with mass m, height h and g is constant gravitational force.

Question : A roller coaster is 94.5 m high at its highest point. What is the maximum possible speed of the roller coaster? The roller coaster’s actual maximum speed is 41.1 m/s.?

Solution :
Height=94.5 metre
Actual maximum speed is 41.1 m/s.
The roller coaster reaches maximum speed when all of its gravitational potential energy has been converted to kinetic energy


Here PE = KE
M*g*h=1/2*m*v²

V²=2*g*h=2*9.8*94.5= 1852.2

V= 43.037 m/sec

The maximum possible speed of the roller coaster, V= 43.037 m/sec


Whenever you have to solve similar kind of question, like finding velocity or any unknown qantities, consider the same formula substitute the values and calculate.

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