Explanation:
The ball is in free fall (gravity is the only force acting on the ball), so its acceleration is 9.8 m/s² down during the entire path.
For idea gases, volume is directly proportional to temperature. That is, an increase in temperature leads to increase in volume and vice versa.
Therefore,
V1/T1 = V2/T2 => T2 = (V2*T1)/V1
Assuming that the balloon is spherical in shape,
V= 4/3*pi*R^3.... In the formula for calculating T2, 4/3*pi cancels out.
R1 = 30/2 15 cm; R2 = 30.5/2 = 15.25 cm; T1 = 20+273.15 =293.15 K
Therefore,
T2 = (R2^3*T1)/R1^3 = (15.25^3*293.15)/15^3 = 308.05 K = 34.9 °C
Answer:
Explanation:
We know that the frequency of the nth harmonic is given by 
, where 
is the fundamental harmonic. Since we have the values of two consecutive frequencies, we can do:
Which for our values means (we do not need the value of <em>n</em>, that is, which harmonics are the frequencies given):
Now we turn to the formula for the vibration frequency of a string (for the fundamental harmonic):
So the tension is:
Which for our values is:
This can be answered using the beat frequency formula, which is simply the difference between 2 frequencies.
Let: <span>fᵇ = beat frequency
</span>f₁ = first frequency
f₂ = second frequency
fᵇ = |f₁ - f₂|
substituting the values:
fᵇ = |24Hz - 20Hz|
fᵇ = 4Hz
The unit Hz also means beats per second, therefore:
<span>fᵇ = 4 beats per second
</span>
Therefore, the answer is C. 4
