Which of the following statements is not true about resonance?
Choose one answer.
a. It is easy to get an object to vibrate at its resonant frequencies but difficult to get it vibrate at other frequencies.
b. A simple pendulum has many resonant frequencies called harmonics.
c. A spring-mass system has only a single resonant frequency.
d. Vibrating strings and air-columns have many resonant frequencies called harmonics.
To determine which of the statements is not true about resonance, we can analyze each option and their validity.
Option a: 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. Resonance occurs when an object vibrates at its natural frequency, which is determined by its physical properties. It is easier to excite an object at its resonant frequency because the amount of energy required to sustain the vibration is lower compared to other frequencies.
Option b: A simple pendulum has many resonant frequencies called harmonics.
This statement is not true. A simple pendulum, consisting of a mass attached to a string, has only one resonant frequency. The oscillation of a pendulum is determined solely by its length and gravitational acceleration, resulting in a single natural frequency.
Option c: A spring-mass system has only a single resonant frequency.
This statement is not true. A spring-mass system can have multiple resonant frequencies. The resonant frequency of such a system depends on various factors, including the mass and stiffness of the spring. Different combinations of these factors can result in distinct resonant frequencies.
Option d: Vibrating strings and air-columns have many resonant frequencies called harmonics.
This statement is true. Vibrating strings and air-columns do have many resonant frequencies, which are often referred to as harmonics. The length, tension, and density of the string or air-column determine the specific frequencies at which resonance occurs.
In conclusion, the statement that is not true about resonance is:
c. A spring-mass system has only a single resonant frequency.