Which of the following statements is not true about resonance?
Answer
It is easy to get an object to vibrate at its resonant frequencies but difficult to get it vibrate at other frequencies.
A simple pendulum has many resonant frequencies called harmonics.
A spring-mass system has only a single resonant frequency.
Vibrating strings and air-columns have many resonant frequencies called harmonics.
not true: A simple pendulum has many resonant frequencies called harmonics.
To determine which statement is not true about resonance, let's analyze each statement:
1. It is easy to get an object to vibrate at its resonant frequencies but difficult to get it to vibrate at other frequencies.
This statement is generally true. When an object is excited at its resonant frequencies, it will vibrate more intensely. However, it is still possible to excite an object at other frequencies, but the amplitude of vibration will be lower compared to the resonant frequencies.
2. A simple pendulum has many resonant frequencies called harmonics.
This statement is also true. A simple pendulum has multiple resonant frequencies or harmonics. Each harmonic corresponds to a multiple of the fundamental frequency.
3. A spring-mass system has only a single resonant frequency.
This statement is not true. A spring-mass system actually has multiple resonant frequencies. The number of resonant frequencies depends on the characteristics of the spring (such as its stiffness) and the mass attached to it. The resonant frequencies can be calculated using the formula: f = 1/2π √(k/m), where f is the frequency, k is the spring constant, and m is the mass.
4. Vibrating strings and air-columns have many resonant frequencies called harmonics.
This statement is true. Vibrating strings and air-columns, such as in musical instruments, have multiple resonant frequencies or harmonics. These harmonics are integer multiples of the fundamental frequency.
Therefore, the statement "A spring-mass system has only a single resonant frequency" is not true about resonance.